Question

In the figure below, a ray OC extends from a point O on a straight line AB. If $\angle$AOC = ${135}^{\circ }$. Find $\left(\frac{\angle BOC}{3}\right)$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so alinear pair of angles must add up to 180 degrees

$\angle$AOC + $\angle$BOC = ${180}^{\circ }$ (linear pair of angles)

$\angle$AOC = ${135}^{\circ }$ (given)

${135}^{\circ }$ + $\angle$BOC = ${180}^{\circ }$

$\angle$BOC = ${180}^{\circ }$ - ${135}^{\circ }$

$\angle$BOC = ${45}^{\circ }$
$\therefore$ $\left(\frac{\angle BOC}{3}\right)$ = $\frac{{45}^{\circ }}{3}$ = ${15}^{\circ }$